# Analytic asymptotic performance of topological codes

@article{Fowler2013AnalyticAP, title={Analytic asymptotic performance of topological codes}, author={Austin G. Fowler}, journal={Physical Review A}, year={2013}, volume={87}, pages={040301} }

Topological quantum error correction codes are extremely practical, typically requiring only a 2-D lattice of qubits with tunable nearest neighbor interactions yet tolerating high physical error rates p. It is computationally expensive to simulate the performance of such codes at low p, yet this is a regime we wish to study as low physical error rates lead to low qubit overhead. We present a very general method of analytically estimating the low p performance of the most promising class of…

## 11 Citations

Performance of topological quantum error correction in the presence of correlated noise

- Physics, Computer ScienceQuantum Inf. Comput.
- 2018

It is found that in the presence of noise correlation, one cannot guarantee arbitrary high computational accuracy simply by incrementing the codeword size while retaining constant noise level per qubit operation, so progressively reducing noise level in qubits and gates is as important as continuously integrating more qubits to realize scalable and reliable quantum computer.

Reconfiguring quantum error-correcting codes for real-life errors

- Computer Science
- 2020

A scheme of decoupling transversal encoded gate errors from state-preparation noise is articulate and experimentally validate its use-case for IBMQ quantum processors and enables quantum CSS code to principally correct longer strings of errors without increasing the codeword size.

Surface codes: Towards practical large-scale quantum computation

- Physics
- 2012

This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer,…

Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes

- Mathematics, PhysicsPhysical Review A
- 2018

One of the most promising routes towards fault-tolerant quantum computation utilizes topological quantum error correcting codes, such as the $\mathbb{Z}_2$ surface code. Logical qubits can be encoded…

Quantum Algorithms, Architecture, and Error Correction

- Mathematics, Physics
- 2018

Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable…

Quantum computing by color-code lattice surgery

- Physics, Mathematics
- 2014

We demonstrate how to use lattice surgery to enact a universal set of fault-tolerant quantum operations with color codes. Along the way, we also improve existing surface-code lattice-surgery methods.…

Universal quantum computation by the unitary control of ancilla qubits and using a fixed ancilla-register interaction

- Physics
- 2013

We characterize a model of universal quantum computation where the register (computational) qubits are controlled by ancillary qubits, using only a single fixed interaction between register and…

Quantum stabilizer codes from Abelian group association schemes

- Mathematics, Physics
- 2014

A new method for the construction of the binary quantum stabilizer codes is provided, where the construction is based on Abelian and non-Abelian groups association schemes. The association schemes…

Constructions of pure asymmetric quantum alternant codes based on subclasses of Alternant codes

- Mathematics, Computer Science2014 IEEE International Symposium on Information Theory
- 2014

It is shown that when dx = 2, Z-parts of the AQCs can attain the classical Gilbert-Varshamov bound, and asymptotically good binary expansions of asymmetric quantum GRS codes are obtained, which are quantum generalizations of Retter's classical results.

Quantum stabilizer codes from Abelian and non-Abelian groups association schemes

- Mathematics
- 2014

A new method for the construction of the binary quantum stabilizer codes is provided, where the construction is based on Abelian and non-Abelian groups association schemes. The association schemes…

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